196 Tlie Examination of Noherfs Nineteenth Band. 



Woodward thinks the ninth band really the narrowest, we may be 

 justified in saying that his hypothesis makes this ratio as great as 

 2^ : 1. Is it for a moment conceivable that a ruhng engine of any 

 sort — to say nothing of one of such exquisite workmanship as that 

 must be which has turned out these miraculous achievements of 

 Mr. Nobert for so many years — should be capable of making errors 

 in its divisions to the extent of one part in thirteen ? 



If we suppose, however, the relation of the spaces in these two 

 bands to be such as Mr. Nobert intended, then the ninth band is 

 not the broader of the two, but the nineteenth. The difference 

 would be -rof^roths of a hne, or xa-wooths — say ^D-woth of an 

 inch. This small space is undoubtedly measurable; but in the 

 present instance it is rather difficult to measure, because, first, the 

 ruled lines themselves are heavier and broader in proportion as the 

 spaces are wider ; and because, secondly, when the lines are truly 

 in focus, the false lines on the margin make it often rather doubtful 

 where the band begins. 



But now, without making any question about the absolute or 

 the relative values of these spaces, any further than to assume that, 

 in the latter particular, the deviation from the intention is not 

 greater than Colonel Woodward supposes, though I am willing to 

 allow it, if necessary, to be as great as 2^ : 1, I think I may 

 reasonably claim that my hst was a perfectly trustworthy one for 

 the purpose for which alone it was appHed, i. e. to settle the ques- 

 tion whether the nineteenth band was or was not truly resolved. 

 Anyone who has studied close rulings under the microscope, with 

 varying obliquity of illumination and parallel rays, will have 

 observed two species of illusion so perfect as to deceive the most 

 practised eye, and even his own if he happens not to know the 

 object at which he is looking. One of these presents the number 

 of lines exactly doubled, and the other shows exactly half the true 

 number. The physical cause of these appearances I believe I am 

 able to explain; but the explanation would be here out of place. 

 Whenever either of these illusive appearances presents itself, the 

 Hnes are perfectly smooth and clear, and continuous from one end 

 of the band to the other. They will inevitably be taken by the 

 unpractised observer for the real lines. But the ordinary appear- 

 ance of the unresolved bands is not this. The spurious lines which 

 appear before resolution are in general rough, irregular, and, to 

 use a word which best expresses the appearance, Uotchy. The 

 number of these rough lines which may be seen in a given band is 

 not very easy to count ; but when I have succeeded to a certain 

 extent in counting, I have found that it is never with me in a 

 simple ratio of 2 : 1, or of 1 : 2 to the number of real lines known 

 to be present. On the other hand the ratio is as inconstant as 

 possible. 



